1. Field of the Invention
Embodiments of the present invention relate to high-performance computing. More particularly, embodiments of the present invention relate to systems and methods for evaluating the convergence to a solution of a matrix equation for stationary method iterative linear solvers.
2. Description of the Related Art
The solution to large-scale matrix equations is often required in a wide variety of scientific and engineering fields. The matrix equation may take the form Ax=b, where A is a known n×n matrix, b is a known vector of size n, and x is an unknown vector if size n. Many times a stationary method iterative linear solver, such as Jacobi, Gauss-Seidel, or variations thereof, is employed to find a solution. The solver may perform a number of iterations, such that during each iteration the solver updates the solution vector. Traditional approaches include allowing the solver to perform a fixed number of iterations. There are a couple of drawbacks to this approach. The solver may perform too few iterations to converge toward a solution, thereby providing an erroneous or inadequate answer. Alternatively, the solver may perform more iterations than are necessary to provide an adequate solution, thus wasting time and unnecessarily utilizing resources.